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Fungrim entry: c12a41

in={1,n≡0(mod4)i,n≡1(mod4)−1,n≡2(mod4)−i,n≡3(mod4){i}^{n} = \begin{cases} 1, & n \equiv 0 \pmod {4}\\i, & n \equiv 1 \pmod {4}\\-1, & n \equiv 2 \pmod {4}\\-i, & n \equiv 3 \pmod {4}\\ \end{cases}
Assumptions:n∈Zn \in \mathbb{Z}
TeX:
{i}^{n} = \begin{cases} 1, & n \equiv 0 \pmod {4}\\i, & n \equiv 1 \pmod {4}\\-1, & n \equiv 2 \pmod {4}\\-i, & n \equiv 3 \pmod {4}\\ \end{cases}

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
ConstIii Imaginary unit
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("c12a41"),
    Formula(Equal(Pow(ConstI, n), Cases(Tuple(1, CongruentMod(n, 0, 4)), Tuple(ConstI, CongruentMod(n, 1, 4)), Tuple(-1, CongruentMod(n, 2, 4)), Tuple(Neg(ConstI), CongruentMod(n, 3, 4))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

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2021-03-15 19:12:00.328586 UTC